36u^2+32u-9=0

Solution for 36u^2+32u-9=0 equation:

36u^2+32u-9=0

a = 36; b = 32; c = -9;
Δ = b2-4ac
Δ = 322-4·36·(-9)
Δ = 2320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{145}}{2*36}=\frac{-32-4\sqrt{145}}{72}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{145}}{2*36}=\frac{-32+4\sqrt{145}}{72}
$